1. Field of the Invention
This invention relates to optical lens systems configured to compensate for chromatic aberration, and particularly to an apochromatic lens suitable for wideband applications.
2. Discussion of the Known Art
U.S. Pat. No. 5,333,076 (Jul. 26, 1994) discloses a stabilized imaging system intended for use in aerial reconnaissance systems, including a fixed lens assembly and a movable electro-optic imager element. The lens assembly has an external entrance pupil located between a rotating prism and a stationary prism, so that the apertures of the two prisms can be made relatively small for a given field of view. In addition, the prisms provide a level of compensation for chromatic aberration that occurs within the lens assembly.
Lens assemblies or systems such as disclosed in the '076 patent are constructed to compensate for chromatic dispersion inherent in each lens element of the system. The systems are typically apochromatic; that is, the lens elements are configured and positioned relative to one another so that the focal length of the lens system is the same at both ends of the light spectrum of interest (achromatic), and at one or more other intermediate wavelengths (apochromatic). Without such compensation, the focal length of the system would change undesirably with the light spectrum received from the object, yielding axial chromatic aberration which causes color fringes to appear at the edges of the projected image of the object. Another example of an apochromatic lens system is disclosed in U.S. Pat. No. 5,973,859 (Oct. 26, 1999). See also U.S. Pat. No. 6,147,815 (Nov. 14, 2000). So-called achromatic lens systems are constructed to obtain the same focal length only at two wavelengths over the spectrum of interest. See, e.g., U.S. Pat. No. 5,959,785 (Sep. 28, 1999).
Chromatic dispersion in a glass lens element occurs because the index of refraction (n) of the glass varies with the wavelength of light transmitted through the glass. The degree of this variation is represented by the so-called Abbe number (V) for a given type of glass. Specifically,V=(nd−1)/(nf−nC);
where nd is the index of refraction of the glass at the wavelength of the helium d line (587.6 nm), nf is the index at the hydrogen f line (486.1 nm), and nC is the index at the hydrogen c line (656.3 nm).
Accordingly, the smaller the value of V, the greater the chromatic dispersion through the glass. Typical Abbe numbers for various types of optical glass are given below:
Glass typeAbbe number (V)SF1125.76LaSFN932.17F236.37BaK157.55BK764.17Fused silica67.8
By combining two lens elements with different Abbe numbers, a lens system can be made to have zero axial chromatic aberration (achromatic correction) for the f and the c lines. These lens systems typically arrange the two lens elements, one positive and one negative, to be in contact or cemented to one another in an arrangement called an achromatic doublet. For the achromatic doublet, the powers and the dispersions of the elements add and are chosen to yield zero total dispersion by satisfying the following equations:Φp/Vp=−Φn/Vn  Eq. 1Φ=Φp+Φn  Eq. 2where
Φ=power of the lens system
Φp=power of the positive lens
Φn=power of the negative lens
ΦVp=Abbe number of the positive lens
ΦVn=Abbe number of the negative lens
A lens system that is corrected for axial chromatic aberration will typically still exhibit some residual chromatic aberration known as secondary spectrum. Secondary spectrum is measured by the difference between the axial position of the system's corrected common f and c line focus point, and the position of the focus point for another wavelength within the spectrum, typically measured at the d line. In this case, the remaining secondary spectrum produces green or purple fringes to appear on images of objects having sharp edges.
The secondary spectrum for a cemented doublet having a focal length (f), is given by:SS=[(−f)(Pp−Pn)]/(Vp−Vn)  Eq. 3where
Pp=partial dispersion of the positive lens
Pn=partial dispersion of the negative lens
and the partial dispersion P for either lens is defined byP=(nd−nf)/(nf−nc)  Eq. 4
For a cemented doublet to have a zero secondary spectrum, the two lens glasses must be chosen so as to have different Abbe numbers but the same partial dispersion. This is very difficult since most glasses exhibit a linear relationship between Abbe number and partial dispersion. By careful selection of glasses, most achromatic doublets can only reduce their secondary spectrum rather than completely eliminating it. To eliminate secondary spectrum completely, apochromatic lens systems typically utilize a minimum of three lens elements, and employ glasses having abnormal partial dispersion, i.e., a dispersion that varies non-linearly with the Abbe number of the glass as explained below. By carefully arranging the powers of the lens elements, their Abbe numbers and partial dispersions, all three lines (f, d, c) can be brought to a common focus point.
Wideband apochromatic lens systems employ the same approach of careful selection of lens element powers, Abbe numbers and partial dispersions. Wideband systems must therefore employ a greater number of lens elements and types of glass due to the extended spectrum, however, and partial dispersions for an extended set of wavelengths must also be considered.
Partial Dispersion and Abnormal Dispersion for General Set of Wavelengths
The relative partial dispersion Px,y for a given type of glass for a general set of wavelengths is defined by:Px,y=(nx−ny)/(nf−nc)  Eq. 5where the subscripts x and y denote standard spectral line assignments associated with specific refractive index values.
The dispersive characteristics of various types of glass may then be compared by plotting the relative partial dispersion Px,y versus the Abbe number V. These quantities share a linear correspondence for most optical glasses and therefore plot along a single straight line. Glasses that exhibit this linear behavior are referred to as normal dispersion glasses. The partial dispersion of these glasses can be approximately described by the following equation:Px,yax,y+bx,y·V  Eq. 6where ax,y and bx,y are constants. Glasses which deviate significantly from the line described by Equation 6 are called abnormal dispersion glasses. For such glass types, the deviation of partial dispersion from the normal line can be represented by the quantity ΔPx,y. A more precise expression for Px,y may then be given by the following equation:Px,y=ax,y+bx,y·V+ΔPx,y  Eq. 7
In their catalogs and publications, suppliers of glass materials typically provide ΔPx,y values as referenced to a straight line defined by the Px,y values for a given type of glass. See, e.g., SCHOTT Technical Information Publication TIE-29, Refractive Index and Dispersion (April 2005); and R. E. Fischer, et al. (OPTICS 1, Inc. and SCHOTT AG), “Removing the Mystique of Glass Selection”, at Internet URL <http:/www.optics1.com/pdfs/removing_mystique.pdf>. Both of these publications are incorporated by reference.
High quality wideband apochromatic lens systems typically employ eight or more lens elements formed from at least five or more different types of glass. This results in a complex lens assembly with higher cost, lower transmittance, and higher susceptibility to glass obsolescence. Consequently, if only one of the required glasses becomes obsolete and a suitable substitute glass cannot be found, a costly redesign often becomes necessary. Because of these disadvantages, a wideband apochromatic lens system that requires fewer lens elements and fewer glass types while offering color correction over a wide spectrum of, e.g., about 400 nm bandwidth, is highly desirable.